A) \[0.5\,Y{{X}^{2}}\]
B) \[0.5\,{{Y}^{2}}X\]
C) \[2Y{{X}^{2}}\]
D) \[Y{{X}^{2}}\]
Correct Answer: A
Solution :
Given: Young's modulus =Y Longitudinal strain =X The potential energy stored is given by \[=\frac{1}{2}\times \text{stress}\,\text{ }\!\!\times\!\!\text{ }\,\text{strain}\] \[=\frac{1}{2}\times Y\times X\times X\] \[=\frac{1}{2}Y{{X}^{2}}\]\[(\because \,stress=\Upsilon \times strain)\] \[=0.5\,\Upsilon {{X}^{2}}\]
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